...Weak gravitational lensing is believed to be the most promising tool to understand the nature of dark matter and to constrain the cosmological parameters used to describe the Universe because it provides a method to map directly the distribution of dark matter (see [6, 61, 70, 1, 64]). From this dark matter distribution, the nature of dark matter can be better understood and better constraints can be placed on dark energy, which aspects the evolution of structures. Gravitational lensing is the process by which light from distant galaxies is bent by the gravity of intervening mass in the Universe as it travels towards us. This bending causes the images of background galaxies to appear slightly distorted, and can be used to extract important cosmological information.

In the beginning of the twentieth century, A. Einstein predicted that massive bodies could be seen as gravitational lenses that bend the path of light rays by creating a local curvature in space-time. One of the rst conrmations of Einstein's new theory was the observation during the 1919 solar eclipse of the detection of light from distant stars by the sun. Since then, a wide range of lensing phenomena have been detected. The gravitational detection of light by mass concentrations along light paths produces magnication, multiplication, and distortion of images. These lensing eects are illustrated by Fig. 2, which shows one of the strongest lens observed: Abell 2218, a very massive and distant cluster of galaxies in the constellation Draco. The observed gravitational arcs are actually the magnied and strongly distorted images of galaxies that are about 10 times more distant than the cluster itself. These strong gravitational lensing eects are very impressive but they are very rare. Far more prevalent are weak gravitational lensing eects, which we consider in this chapter, and in which the induced distortion in galaxy images is much weaker. These gravitational lensing eects are now widely used, but the amplitude of the weak lensing signal is so weak that its detection relies on the accuracy of the techniques used to analyze the data. Future weak lensing surveys are already planned in order to cover a large fraction of the sky with high accuracy, such as Euclid. However improving accuracy also places greater demands on the methods used to extract the available information...

In short the weak lensing is closer to a full random gaussian measurement matrix as opposed to the sparse strong lensing measurement matrix. Since events behind these lenses are somewhat deterministic I wonder how new techniques in low rank approximation will help in the determination of the weak lenses property or how this lens can be calibrated.